That police should ONLY break up violent protests

Your initial post appears to be an argument, as opposed to an acceptance round. Thus, I will treat it accordingly.

Arguments

A1. Protests are generally considered protected under the First Amendement Right known as Freedom of Assembly (or, interchangeably, Freedom of Association). It essentially gives us the right to peaceably assemble. it also gives us the Right to appeal to the government for assistance with relief from grievance (1). This is an important Right, and a lot of precedent has been set to help narrow down what specifically it protects. For example, in Virgina vs Hicks (2), the Supreme Court unanimously ruled that what was essentially construed as loitering is not protected by the Constitution. However, in Edwards vs South Carolina (3), it was made clear that peaceably assembling to support a view, no matter how unpopular it is, reflects the right our Bill of Rights aims to protect in its purest sense.

A2. Blocking traffic in general is illegal, and separate from Bill of Rights protections. It violates the modifier "peaceably." On the other hand, police officers should be treating protestors as citizens like any other, and should render due warnings. On the other hand, in New York City, during the Occupy Wall Street protests, the police may have actually been the cause of the blocked traffic in the first place, making those arrests unconstitutional (4).

Rebuttals

R1. The only occassion during which the Occupy Wall Street protestors blocked a bridge was on the 2nd of October, when more than 700 protestors were arrested for walking across the bridge, blocking a single lane of traffic "for hours." Many of the protestors there claimed that they were actually instructed by the NYPD to walk on the street in the first place (4).

R2. Simply stating that something occurred does not prove that it was right. Indeed, the NYPD arrested over 700 protestors that day, and it may have been an abortion of justice.